Short Answer
The combined gas law explains the relationship between pressure, volume, and temperature of a gas when the amount of gas remains constant. It combines three important gas laws—Boyle’s law, Charles’s law, and Gay-Lussac’s law—into one equation.
According to the combined gas law, if any two properties change (pressure, volume, temperature), the third property adjusts to keep the relationship balanced. This law helps us understand how gases behave when more than one factor changes at the same time.
Detailed Explanation
Combined Gas Law
The combined gas law is a single equation that joins three major gas laws: Boyle’s law, Charles’s law, and Gay-Lussac’s law. These laws describe how pressure, volume, and temperature affect gas behaviour. When combined, they give a complete picture of how a gas responds when more than one condition changes. The combined gas law is useful because in real-life situations, temperature, pressure, and volume often change together, not one at a time.
This law works under the condition that the amount of gas (number of moles) remains constant. It helps chemists, engineers, and students understand how gases behave in closed systems when external factors like heating, cooling, compression, or expansion occur.
Relationship Between Pressure, Volume, and Temperature
The combined gas law shows that pressure, volume, and temperature are all linked. If one of these quantities changes, it affects the others. This law states that:
- Pressure is inversely related to volume (Boyle’s law)
- Volume is directly related to temperature (Charles’s law)
- Pressure is directly related to temperature (Gay-Lussac’s law)
The combined gas law brings all these relationships together in one formula.
Mathematical Expression of Combined Gas Law
The combined gas law is written as:
P₁V₁ / T₁ = P₂V₂ / T₂
Where:
- P₁ = initial pressure
- V₁ = initial volume
- T₁ = initial temperature
- P₂ = final pressure
- V₂ = final volume
- T₂ = final temperature
Temperature must always be measured in Kelvin.
This equation shows that when the initial and final states of a gas are compared, the ratio of pressure × volume to temperature stays constant.
Why the Combined Gas Law Works
The combined gas law works because it is based on the motion of gas particles. Gases behave in predictable ways when heated or cooled, or when compressed or allowed to expand.
- When temperature increases, gas particles move faster, causing higher pressure or larger volume.
- When temperature decreases, particles move slowly, causing pressure and volume to decrease.
- When volume decreases, particles collide more with container walls, increasing pressure.
- When volume increases, collisions decrease, reducing pressure.
The combined gas law reflects all these relationships in a single mathematical statement.
Understanding Through Each Component Law
- Boyle’s Law (P ∝ 1/V):
At constant temperature, pressure increases when volume decreases. - Charles’s Law (V ∝ T):
At constant pressure, volume increases when temperature increases. - Gay-Lussac’s Law (P ∝ T):
At constant volume, pressure increases when temperature increases.
The combined gas law shows how all these effects happen together if none of the variables are kept constant except the amount of gas.
Everyday Examples of Combined Gas Law
The combined gas law can be seen in many common situations where temperature, pressure, and volume change at the same time.
- Hot Air Balloons:
When the air inside the balloon is heated, temperature rises, volume increases, and pressure adjustments allow the balloon to lift off. - Car Tyres:
Tyre pressure changes with outside temperature and driving conditions. Pressure increases when temperature rises and decreases when it becomes cold. - Pressurised Spray Cans:
When a spray can is heated, both pressure and temperature increase. When used, releasing gas reduces volume and affects pressure. - Weather Balloons:
As balloons rise, pressure decreases and temperature changes, causing the balloon to expand due to changes in volume. - Air in a Sealed Container:
If a sealed container is heated, the temperature increases, pressure rises, and the container may expand slightly depending on its strength.
Importance of Combined Gas Law in Science
The combined gas law is a foundational tool in chemistry and physics. It helps in:
- calculating unknown gas properties during experiments,
- predicting gas behaviour under changing conditions,
- designing pressure-based equipment,
- understanding atmospheric processes,
- studying thermodynamics and gas reactions.
It serves as a bridge to the ideal gas equation, which includes the number of moles and gives a more complete understanding of gas behaviour.
Conclusion
The combined gas law combines Boyle’s law, Charles’s law, and Gay-Lussac’s law into one relationship. It states that the ratio of pressure × volume to temperature remains constant when the amount of gas is unchanged. This law explains how gases behave when more than one condition—pressure, volume, and temperature—changes at the same time. It is widely used in laboratories, industries, and everyday life to understand and predict the behaviour of gases.